After the first order to fire I find no logic reason to make the archers wait:
1 Different archers have different speed at reloading their bow, you are basically making the fast ones fire less arrows than what they could or you are giving the order when the slow ones are not ready which means they dont shoot and again, less arrows are shot.
2 If you have an enemy with shields and coordinations (let's say Roman soldiers) pushing into you, by firing all arrows at the same time you are making a huge cloud of arrows that will make them use their shields efficiently resulting in a low ammount of casualties, on the second hand if after the first call all archers fire at their own rate there is no way to just say: "Dude huge cloud of arrows incoming just stop moving and shields up for a sec, okay done push again" you can not really defend yourself if the fire rate its random because either you dont move at all and stand deffending the arrows til you run out of soldier or they run out of arrows or you are forced to keep moving and you will lose a lot of soldiers one by one because you couldnt go into formation.
I see this everywhere in TV, from series to anime, movies so on. Therefore, is this bs that hollywood created and made popular or am I missing something out on the reasoning to time each and every wave of shots?
You pretty much answered your own question for the reasons you specified.
We should first consider how archers were deployed in battle. Hollywood (and video games) likes to make use of large formations of archers shooting in perfect synchronisation. However, this is largely not how archers were used in most kinds of warfare. Often, archers were more organic and deployed with more fluidity, such as "light infantry" in ancient Greek warfare, to the hordes of horse archers of the steppe nomads. The use of archers in massed formations is more typical of medieval warfare, specifically England, from which much of modern perspectives of archery are derived.
The act of holding onto the shot was detrimental to the shot itself, due to the heavy draw weights of bows, such as the English longbow. At over 100lbs on the fingers, it was unrealistic to hold the draw any longer than necessary. Inexperienced archers might hold for longer to take more came in the aim, while veteran archers held for shorter and achieved a "sharp release", our understanding being that holding too long onto the shot will lead to contractions in the muscles, a loss of power through a collapse in the archer's frame, and ultimately a weaker shot. Even in modern archery, we discourage long holds for this reason.
Furthermore, historical archery sources often emphasise the need to draw and release as quickly as possible for additional power. The Byzantine manual Strategikon states that "speed is important in shaking the arrow loose and discharging it with force". The Archer's Guide (1833) makes reference to how "drawing and shooting should be done in one continued action throughout", while Toxophilus by Roger Ascham describes the release as "quick and hard". In Turkish archery, several methods are described: Ikhtilas, referring to drawing and rapidly and loosing without pause as soon as the hand reaches the ear, and mefruk, in which the arrow is drawn slowly, then suddenly drawn back and then "jerked back like lightning". This is reinforced in Arab Archery, which claims that an expert archery must loose "at the full draw without stop, delay or pause".
The basis of this is one of two things: that this affects the archer's ability to deliver a clean, strong shot without loss of power from physical fatigue, or the principle of elastic hysteresis, in which the bow loses energy due to internal friction the longer it is held at draw. Thus, as far as historical technique goes, it is generally beneficial, if not required, to draw and shoot in a single motion and thus any coordinating shooting that prevents this execution goes against the manuals and training that we are aware of.
The second major thing to consider is that such coordination would not be possible. With thousands of archers on the battlefield, there was no way to synchronise. Archers were not always deployed together in a single unit, and if they were, the line would have stretched very far. There might be banners and drum calls - at Agincourt, the call "Nestroque" was used to signal the archers to commence shooting, and perhaps there might be calls of "nock" and "mark", but the action of drawing and loosing were understood to be one motion and archers did not hold until they were told to shoot - that was something that was implied when the order to draw was given. As each archer had their own action and shot at their own pace, anything after the initial volley would turn into a steady shower of arrows. Indeed, from descriptions of the "arrow storm" at Agincourt, it makes more sense that a "shower" of arrows would be continuous, not sporadic.
However, I do want to provide a rebuttal to the "but, shields!" reasoning. It has been conjectured by Mike Loades in his work on English archery that this might have been a downside of coordinated volleys. However, I'm not so certain whether this would have made a huge impact. Firstly, not every soldier had shields, or had shields of sizes that were capable of blocking arrows, or thick enough to prevent arrows going through. The Scottish schiltron formations, for example, were armed with pikes, and though the front ranks might have been well-armoured, the same could not be said for the rest of the formation who were shot to pieces at Falkirk. Nor did continuous fire have an advantage against shielded enemies. The Romans at Carrhae were pinned by Parthians, and their testudo formation largely protected them from arrows despite not shooting in volleys, and they were ultimately defeated by repeated charges by cataphracts and attrition from the constant arrow showers from resupplied horse archers. This isn't like hearing artillery coming in and taking cover. Even if you could see the arrows coming, there was only so much you can do to not get hit, regardless of whether the shots were coordinated or erratic.
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